Question: A circle has a sector with area $12\pi$ and central angle $270^\circ$. What is the area of the circle? ${16\pi}$ $\color{#9D38BD}{270^\circ}$ ${12\pi}$
Solution: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{270^\circ}{360^\circ} = 12\pi \div A_c$ $\dfrac{3}{4} = 12\pi \div A_c$ $A_c \times \dfrac{3}{4} = 12\pi$ $A_c = 12\pi \times \dfrac{4}{3}$ $A_c = 16\pi$